Average Error: 0.3 → 0.3
Time: 3.1s
Precision: 64
\[\frac{\left(x.re \cdot y.im\right)}{\left(x.im \cdot y.re\right)}\]
↓
\[x.re \cdot y.im + x.im \cdot y.re\]
\frac{\left(x.re \cdot y.im\right)}{\left(x.im \cdot y.re\right)}
↓
x.re \cdot y.im + x.im \cdot y.re
double f(double x_re, double x_im, double y_re, double y_im) {
        double r571321 = x_re;
        double r571322 = y_im;
        double r571323 = r571321 * r571322;
        double r571324 = x_im;
        double r571325 = y_re;
        double r571326 = r571324 * r571325;
        double r571327 = r571323 + r571326;
        return r571327;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r571328 = x_re;
        double r571329 = y_im;
        double r571330 = r571328 * r571329;
        double r571331 = x_im;
        double r571332 = y_re;
        double r571333 = r571331 * r571332;
        double r571334 = r571330 + r571333;
        return r571334;
}

Error

Bits error versus x.re

Bits error versus x.im

Bits error versus y.re

Bits error versus y.im

Derivation

  1. Initial program 0.3

    \[\frac{\left(x.re \cdot y.im\right)}{\left(x.im \cdot y.re\right)}\]

  2. Final simplification0.3

    \[\leadsto x.re \cdot y.im + x.im \cdot y.re\]

Reproduce

herbie shell --seed 2019124 +o rules:numerics
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, imaginary part"
  (+.p16 (*.p16 x.re y.im) (*.p16 x.im y.re)))